Quantity (REF ) is a straightforward weighted generalization of the RV coefficient [1]}, [2]}:
consider multivariate features \(\mathbf {X}\in \mathbb {R}^{n\times p}\)  and \(\mathbf {Y}\in \mathbb {R}^{n\times q}\) , directly entering into the
definition of \(\mathbf {D}_X\)  and \(\mathbf {D}_Y\)  as coordinates, or equivalently as \(\mathbf {K}_X=\sqrt{\mathbf {\Pi }}\mathbf {X}_c\mathbf {X}_c^\top \sqrt{\mathbf {\Pi }}\)  and \(\mathbf {K}_Y=\sqrt{\mathbf {\Pi }}\mathbf {Y}_c\mathbf {Y}_c^\top \sqrt{\mathbf {\Pi }}\) , where \(\mathbf {X}_c=\mathbf {H}\mathbf {X}\)  and \(\mathbf {Y}_c=\mathbf {H}\mathbf {Y}\)  are the centered scores.
